# Magnetic Circuit

The magnetic circuit will be outlined as, the closed path derived by the magnetic lines of force i.e. flux. Such a magnetic circuit is associated with completely different magnetic quantities as m.m.f, flux reluctance, permeableness etc.

Think through simple magnetic circuit shown within the Fig. This circuit involves an iron core with cross-sectional are of 'a' in m2 with a mean length of 'l' in m. A coil of N turns is wound on one in all the perimeters of the sq. core which is excited by a source. This source drives a current I through the coil. This current carrying coil produces the flux (Ð¤) that completes its path through the core as shown within the Fig.

This is analogous to meek electrical circuit within which a supply i.e. e.m.f. of E volts drives a current I that completes its path through a closed conductor having resistance R. This analogous circuit is shown within the Fig.
Let us derive relationship between m.m.f, flux and reluctance.
I = Current flowing through the coil.
N = Number of turns.
Ð¤ = Flux in webers.
B = Flux density in the core.
Âµ = Absolute permeability of the magnetic material
Âµr = Relative permeability of the magnetic material

Magnetic field strength inside the solenoid is given by,
H = (NI/l) AT/m

Now flux density is, B = ÂµH
B = [(Âµo Âµr NI)/ l] Wb/m2
Now as area of cross section is “a” m2,
∴ Total flux in core is,
Ñ„ = Ba
Ñ„ = [(Âµ0 Âµr NI a)/l] Wb
i.e. Ñ„= (NI)/(l/ Âµ0 Âµr a)
Ñ„ = m.m.f. / reluctance
Ñ„ = F/S
Where,
NI = F (Magneto motive force m.m.f in AT)
S= (l/Âµ0 Âµr a) (Reluctance offered by the magnetic path).

This expression of the flux is very much similar to expression for current in electric circuit.
I = e.m.f / resistance